In a typical gas turbine engine (GTE), one or more fuel injectors direct a liquid or gaseous hydrocarbon fuel into a combustion chamber (called combustor) for combustion. The combustion of hydrocarbon fuels in the combustor produce undesirable exhaust constituents such as NOx. Different techniques are used to reduce the amount of NOx emitted by GTEs. In one technique, a lean premixed fuel-air mixture is directed to the combustor to burn at a relatively low combustion temperature. A low combustion temperature reduces NOx formation. In another technique, steam is directed to the combustor to reduce the temperature and reduce NOx production. U.S. Pat. No. 7,536,862 B2 to Held et al. (the '862 patent) describes a fuel injector for a gas turbine engine in which fuel is injected from the fuel injector into the combustor through primary and secondary openings. Steam is injected alongside the fuel to decrease the temperature of the flame in the combustor, and thereby reduce NOx production.